This error calculator compares an observed value with a nonzero accepted reference and shows the error magnitude and signed deviation.
Compare a measurement with its accepted reference
Enter the observed measurement and a known accepted reference using the same unit. The reference cannot be zero. The main result is the nonnegative magnitude of the reference-relative discrepancy; the separate signed rows preserve the direction of the comparison.
The accepted value must be known independently. Two equally uncertain measurements do not supply an accepted reference merely because one is entered in that field.
Signed deviation here is observed minus accepted, divided by the signed accepted reference. Absolute error uses the magnitude of the reference.
Percent error worked example
An observed value of 48 is compared with an accepted reference of 50. The signed measurement difference is -2. The tool returns 4% absolute error and -4% signed relative deviation.
The absolute discrepancy is divided by the magnitude of the reference and multiplied by 100. Using the observed value as the denominator would answer a different question.
Absolute error and signed deviation
The main error magnitude is always nonnegative. Signed deviation can be negative or positive. NIST documents both signed subtraction orders and the absolute-value convention, so identify the convention when comparing answers from different tools.
For observed 105 and accepted 100, absolute error is 5%, with 5% signed deviation. For observed -48 and accepted -50, the absolute error remains 4%, while the signed measurement difference is 2 and signed relative deviation is -4%. A negative reference changes how a relative sign relates to the signed measurement difference.
Error can exceed 100%: observed 4 compared with accepted 1 gives 300%. For equally ranked peer measurements, use difference in the Percentage Calculator instead of treating one as an accepted reference.
For a gap between percentage rates, the Percentage Point Calculator labels the signed difference in points. The Ratio Calculator simplifies compatible quantities and solves a missing proportional term.
A valid reference is different from measurement uncertainty
A zero reference makes reference-relative error undefined, so the calculator rejects it even when the observed value is also zero. A known reference with a negative value is supported: the absolute result divides by its magnitude, while the labeled signed deviation divides by the signed reference.
The calculation does not estimate measurement uncertainty, identify a true value, or decide whether an error is acceptable. A meaningful tolerance or significance conclusion requires the measurement context and an appropriate method.
Integer fractions, decimals and scientific notation are calculated exactly. Approximate decimals are marked and shown to 6 places. Inputs allow 64 raw characters, 12 decimal places, exponents between -12 and 12, and at most 15 digits per fraction integer. The maximum absolute input is 1000000000000; a tiny nonzero reference can produce a much larger error percentage.